Obviously I have no personal experience with this particular car, but in typical sequential race transmissions, the clutch pedal is only for launching the car. Once you're rolling, you just bang the lever to shift it. On downshifts, you do blip the throttle to get the shift, but without clutch--even when you're on the brakes.

Actually a Porsche driver in the ALMS stated that he clutches when he downshifts so that he can perform said throttle blip. Otherwise he'd be blipping the throttle with a lower gear engaged.